8 cubes can be joined face-to-face to form a closed ring with a hole in it, with each cube sharing a face with only two others. The same can be done with 8 dodecahedrons. Is the same possible with the other platonic solids? What is the minimum number of each solid needed to form such a loop?

Given a convex regular d-polytope, is there a general way to determine if N instances of it can form a loop, by gluing their d-1 dimensional faces together? (Assuming the loop has a hole and no two objects intersecting, ie no two objects share a d-volume).
And is there a way to compute the minimum N needed for this?